S P HI I


L U 09k T


Qudrantalt. Hence if the two Sides be 1s than a Ojuadrant,
the two Angles are acute.
14. If in a Spherical Wringle; the feveral Sides be each
greater than a Quadrant; or only two of them greater, and
the Third equal to a Quadrant £ the feveral Angles are
obtufe.
15. If in an obliquangular Spherical 1rianglej two Sides
be lefs than a Quadrant, and the Third greater; the Angle
oppofite to the greatefi will be obtufe, and the refit acute.
Refoluticn of SPHERICAL'Triavgles. See TRIANGLE.
SPHERICAL Geormetrv, the Dodrineof the Sphere; parti-
cularly of the Circles described on the Surface thereof, with the
Method of projeding the fame on a Plane. See SPHEERICRS.
SPHERICAL f'rzgo02cmetry, the Art of refolving Spherical
Yfriavgles; i. e. from three Parts of a Spherical Triangle given,
to find the re{d. E.gr. From two Sides of one Angle; to
find the other two Angles, and the third Side. See SPHE-
APICAL Ylriavgle and TRIGONOMETRY.
SPEHERICAU A4ftronomv, that Part of Afironorny which
confiders the Univerfe, fuch as it appears to the Eye. See
- ASTRONOMY.
Under Spherical Aironomzy, then, come all the Phamnomena
and Appearances of the Heavens and heavenly Bodies, fuch
as we perceive them; without any Inquiry into the Reafon,
the Theory, or the Truth thereof: by which it is diffinguilh-
ed from  'lheorical 4Afronomy, which  confiders the real
Strudure of the Univerfe, and the Caufe of thofe Phxno-
mena.
In the Spherical Afgronomy, the World is conceived to be
a concave, fpherical Surface, in whofe Centre is the Earth,
or rather the Eye, about which the vifible Frame revolves,
with Stars and Planets fix'd in the Circumference thereof.
And on this Suppofition all the other Phznomena are deter-
mined.
The f7Jeorical Aftronormy teaches us, from the Laws of
Opticks, fec. to correft this Scheme, and reduce the whole
to a gufter Syflem. See SYSTEM.
S HERICITY, the Quality of a Sphere; or that whereby
a thing becoms Spherical, or round. See SPHER E.
The Sphericity of Pebbles, Fruits, Berries, Ee. of Drops
of Water, Quick-filver, E.c- of Bubbles of Air under Water,
s.igc. Dr. Hook takes to arit from the Incongruity of their
Particles with thofe of the ambient Fluid, which prevents
their Coalefcing; and by preffing on them, and encompafling
them all around equally, turns them into a round Form. See
DROP.
This, he thinks, appears evidently, from the Manner of
making fmalrround Shot of feveral Sizes, without caPling the
Lead into any Moulds; frotw Drops of Rain being form'd, in
their fall, into round Hail-flones; and from Drops of Water
falling on fmall Duff, Sand, Eec. which firait produce an
artificial round Stone; and 'from the fmall, round, red-hot
Balls, form'd by the Collifion or Fufion of Flint and Steel,
in firiking Fire.
But all thefe Cafes of Sphericity feem better accounted for,
from the great Principle of Attraftion; whereby the Parts
of the fame Fluid drop, &ec. are all naturally ranged as near
the Centre as poffible, whith necefflarily induces a fpherical
Figure: and, perhaps, a repelling Force between the Particles
of the Drop, and of the Medium, contribute not a little
thereto. See ATTRACTION.
SPHERICKS, the liofrine of the Sbphere, particularly of
the feveral Circles defcribed on the Surface thereof; with
the Method    of projeffing  the  fame in  Plano.  See
SPHERE.
The principal Matters fhewn herein, are as follow
x. If a Sphere be cut in any Manner, the Plane of the
Seaion will be a Circle, whofe Centre is in the Diameter of
the Sphere.
Hence, i , The Diameter H I(Tab. Trigon. Fig. i7.) of a
Circle, paffing through the Centre C, is equal to the Diameter
A B of the generating Circle; and the Diameter of a Circle,
as FE, that does not pafs through the Centre, is equal to fome
Chord of the generating Circle.
Hence, 20, As the Diameter is the greatefi of all Chords;
a Circle paging through the Centre, is the greatefl Circle of the
Sphere; and all the red are lever than the fame.
30 Hence, alfo, all great Ctrcles of the Sphere are equal to
one another.
i. Hence, alfo, if a great itcle of the Sphere pafs through
any given Point of the Sphere, as A5 it muft alfo pals
through the Point diametrically oppolite thereto, as B.
f- If Two great Circles mufually interfe& each other, the
Line of the Seation is the Dias~ter of the Sphere, and there-
fore two great Circles inter1each other in Points diametri-
cally oppofite.
6f A great Circle of the pre, divides it into two equal
Parts or Hemifpheres.
2. All great Circles of the here cut each other into two
Parts; and, converfely, all C  es that thus cut each other,
are great Circles of the Sphy
3. An Arch of a great Ci7  of the Sphere, intercepted


Si   F1 1


between another ,Arch H IL (Fig, i 8.) ahd its Poles A and a
is a Quadrant.
That intercepted between a lefis Circo DE F, and, one of
its Poles A, is greater than a Quadrant; and that between
the fame and the other Pole B, lefs than a Quadrant - and,
converfely,
4. If a great Circk of the Splhere pafs through the Poles ot
another, that other pafts through the Poles of this. Andt if
a great Circle pafs through the Poles of another, the Two
cut each other at right Angles, and converfely.
S. If a great Circle, as A F B D, pa&s through 'the 'Poles
A and B of a lefer Circle D E F, it cuts it into equal Parts s
and at right Angles.
6. If two great Circles AE B F and C E DF (Fig. i9.) in-
terfeft each other in the Poles E and F of another great Circle
A C BD D that other will pafs through the Poles H and h,
I and i of the Circles AEBF and CEDF.,
7. If two great Circles A E B F and C ED F, cut each other'
mutually; the Angle of Obliquity A E C, will be equal to
the Diffance of the Poles H 1.
8. All Circles of the Sphere, as G F and LK   (Fi. 20.)
equally diflant from its Centre C, are equal, and the k rther
they are -removed from the Centre, the lefs they are. Hence,
fince of all parallel Chords, only two, D E and E K are equally
diflant from the Centre ;5 of all the Circles parallel to the fame
great Circle, only two are equal.
9. If the Arches F H and K H, and GI and IL, inter-
cepted between a great Circle I M H and the leffer Circles
G N F and LO K; be equal, the Circles are equal.
io. If the Arches F H and G I of the fame great Circle
AIBH, intercepted between two Circles G N F and I M H,
be equal, the Circles are parallel.
i x. An Arch of a parallel Circle I G (Fig. 2 T.) is fimilar
to an Arch of a great Circle A E; if each be intercepted
between the fame great Circles C A F and C E F.   --
Hence the Arches A E   and I G, have the fame Ratio to
their Peripheries; and, confequently, contain the fame Num-
ber of Degrees. And hence the Arch I G is lefs than the
Arch A E.
iz. The Arch of a great Circle, is the fhorteft Line which
can be drawn from one Point of the Surface of the Sphere to
another: And the Lines between any two Points on the fame
Surface, are the greater, as the Circles whereof they are
Arches, are the lefs.
Hence, the proper Meafure, or Diflance of two Places on
the Surface of the Sphere, is an Arch of a great Circle inter-
cepted between the fame.
SPHEROID, in Geometry, a Solid approaching 'to the
Figure of a Sphere, but not exactly round, but oblong; as
having one of its Diameters bigger than the other; and gene-
rated by the Revolution of a Semi-ellipfis about its Axis.  I
When 'tis generated by the relation of the Semi-ellipfis about
its greater Axis, 'tis call'd an Oblong Spheroid; and when
generated by the Revolution of an Ellipfis about its les Axis,
an oblate Spheroid. See OBL ATE.
The Contour of a Dome, tDaviler obferves, fhould be
Half a Spheroid. Half a Sphere, he fays, is too low to have
a good Eaea below. Ste DOME.
For the Solid Dimenfions of a Spheroid, 'tis T of its Circum-
fcribing Cylinder: Or it is equal to a Cone, whore Altitude is
equal to the greatet Axis, and the Diameter of the Bafe to
four Times the lefs Axis of the generating Ellipfis.
Or a Spheroid is to a Sphere defcribed on its greater Axisj
as the Square of the lels Axis to the Square of the. greater
Or 'tis to a Sphere defcribed on the lerer Axis, as  i greater
Axis to the Eels. The Word is form'd from     Spheera, and
AP&, Shape.
SPHINCTER, in Anatomy, a Term applied to a kind of
circular Mufcles, or Mulcles in Form of Rings, which ferve to
clofe~and draw up feveral Orifices in the Body, and prevent
the Excretion of the Contents. See MUSCLE.      ,I
The Word is form'd from the Greek   zlix'nf, stri~or, i. e.
romething that binds and confiringes a Thing very clofely;>
thefe Mufcles having an Eaf:& much like that of a Purfe-
firing.
SPHINCTER Ani, is a circular Mufcle, ferving tofhut the
Anus, and keep the Excrements from coming away involun-
tarily. See ANUS and EXCREMENTS.
'Tis near two Inches broad, and hangs down below the
Reaum, near an Inch. It is faflen'd on the Sides to the Bones
of the Coxendic, and behind to the Os facrumn: Before, in
Men, to the Accelerator Urine, and in Women, to the Vagina
Uteri. See RECTUM.
Some would have it Two Mufcles, and fome Three; but
without much Reafon.
SP HINCTER effict, is a Muflecoxififling of circular ribres,
placed at the Exit of the Bladder. to prevent the perpetual
dripping of the Urine. SeeURINE and BLADDER.
It keeps the Bladder conflantly Ihut; and is only opened,
when by the Contraffion of the Abdominal Mufcles, the
Bladder is comprefs'd, and the Urine forced out.


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SPHINCT.R,